Disney shares also got a boost earlier this month when the company reported strong quarterly earnings. Disney's film studio helped fuel the company's 22% increase in net income for its fiscal third quarter, although its cash cow ESPN sports empire suffered from rising sports rights fees, which weighed down results of the company's television division.

Disney posted net income of $2.25 billion for the quarter that ended June 28, up from $1.85 billion a year earlier. Revenue increased 8% to $12.47 billion.

The company's earnings were released the same day that Rupert Murdoch's 21st Century Fox abandoned its bid for rival media company Time Warner.

Fox's short-lived run for Time Warner, and subsequent withdrawal of its offer, caused media stocks to fluctuate.

Fox's shares have recaptured ground they lost during the company's run for Time Warner. Fox Class A shares closed Tuesday at $35.89.

Time Warner shares are up nearly 8% from their pre-Fox-bid levels. Time Warner shares closed Tuesday at $76.99. (Shortly after Fox's bid was disclosed in mid-July, Time Warner reached $87 a share)

Disney's 52-week low of $60.41 came last year.

Disney's current market capitalization is nearly $155 billion.

The second-largest media company, Comcast Corp., which owns NBCUniversal, has a market cap of $141 billion.